Critical bandwidth and consonance in relation to cochlear frequency-position coordinates

Abstract

A recent paper (Greenwood, 1990) has reviewed some of the data in the literature on the frequency-position coordinates of the cochlear partition in a number of species and the degree to which they are fitted by empirical functions developed in 1961 (Greenwood, 1961b, 1974b). Continued confirmation by physiological data makes this frequency-position function more independent of non-physiological data and provides a more secure means of testing possible relations of psychoacoustic data to cochlear coordinates. The present paper reviews various sets of critical band, or similar, data in humans and other species and finds that a considerable body of bandwidth estimates correspond to equal distances along the cochlear partition (on this assumption), conforming also to an exponential function of distance. As shown in 1961. such a function would imply that the same set of bandwidths is also a linear function of frequency. Some of the early critical bandwidth, and also 'consonant interval', estimates in man correspond to equal distances on the cochlear partition to a degree not generally recognized. Thus above about 300 to 500 Hz most of the critical band data (of Zwicker and Gassier collated by Zwicker et al., 1957), correspond quite well to equal distances on the Békésy-Skarstein cochlear map fitted by the frequency-position function, as opposed to the values published in the critical band table or curve (which do not do so above 3 kHz). Consonant interval data tend to correspond closely to equal distances, from below 100 Hz to about 3 kHz. Certain post-1961 'critical band' (ERB) estimates collated by Moore and Glasberg (1983) and extended by Moore et al. (1990) and Shailer et al. (1990) also correspond quite closely to constant distances calculated by the 1961 function. So too do some, but not all, of the frequency intervals shown by Plomp (1964) and Plomp and Mimpen (1968) to be required to resolve the components of a harmonic complex. Some critical bandwidth data from animal studies may also correspond approximately to equal distances. This survey of old and new results, plotted on a rational distance scale, may assist in explaining what potential mix of factors operates to determine the estimated bandwidths when the values differ across experiments or in different frequency ranges. The correspondence, in the preponderance of cases, of critical bandwidth to a constant distance may facilitate an understanding of the operational definitions of critical bandwidth in different experiments and of the common underlying mechanisms. The correspondence is consistent with the basic explanation of critical bandwidth and consonance offered in Greenwood (1971, 1972b. 1974b) and Greenwood et al. (1976). The critical bandwidths measured in pure-tone masking (the masker-notch interval), two-tone masking, two-tone dissonance-consonance judgments. AM and Quasi-FM detection, narrow-band masking, and two-band (notchednoise) masking reflect a common pattern of nonlinear effects, related to approximately constant 'dimensions' of the region of cochlear nonlinear input-output functions and accelerated phase accumulation (Greenwood, 1974b, 1977), and are codetermined by combination tones and an asymmetrical pattern of suppression (Greenwood and Goldberg, 1970), the latter being incorporated in a gain control mechanism (Greenwood, 1986a, b, c; Greenwood, 1988).